Jermain Defoe received a standing ovation from the Spurs fans when he was paraded on the pitch just before kick-off after completing a £15million move from Portsmouth.
The Tottenham players were clearly boosted by his arrival and despite falling behind to an early goal from Martin Paterson, strikes from Michael Dawson, Jamie O'Hara, Roman Pavlyuchenko and own goal from Michael Duff ensured Spurs have one foot in the final at Wembley on March 1.
Defoe will be able to play in the second leg at Turf Moor and Harry Redknapp must fancy his chances of picking up his second major trophy inside the space of 12 months after steering Portsmouth to FA Cup success last season.
After knocking out Fulham, Chelsea and Arsenal on route to the semi-finals, Burnley looked like they were going to cause another major upset when they opened the scoring after 14 minutes.
The impressive Chris Eagles cut inside Gareth Bale and crossed for Paterson, who was unmarked at the far post and he had the easy task of knocking the ball into an empty net.
Tottenham finally woke up and almost snatched an equaliser on 25 minutes. Jonathan Woodgate flicked the ball in to Pavlyuchenko, who saw his close-range shot produce a stunning save from Brian Jensen diving away to his right.
The Spurs players were booed off the pitch at half-time and Redknapp was determined to change things around by bringing on O'Hara for the ineffective David Bentley.
The move paid off as Tottenham grabbed an equaliser just a minute into the second half when Dawson rose above Clarke Carlisle to head the ball into the corner of the net.
Tottenham looked a completely different team and took the lead on 52 minutes.
Pavlyuchenko's ball was flicked on by Luka Modric and O'Hara saw his shot slip through the hands of Jensen in the Burnley goal.
Burnley tried everything to get themselves back into the game and had a golden chance on 64 minutes when Robbie Blake's cross was cleared off the line by Bale.
Burnley were made to pay just 60 seconds later when Tottenham added a third.
Bale picked out Pavlyuchenko, who cut inside Carlisle and drilled the ball into the corner of the net. The Russian international has now scored in every round of the Carling Cup this season.
Tottenham looked to have put the tie beyond Burnley when they added a fourth on 67 minutes.
O'Hara's free-kick was headed into his own net by Michael Duff to ensure a memorable night for both Defoe and the Tottenham supporters.